Location, Network Design and Routing with Relays

Location, Network Design and Routing with Relays

Operations Seminar by Hande Yaman Paternotte (KU Leuven)

March 2019, Monday 25 (03:00 pm) - BN1 -1711

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With different names and characteristics, relays play a crucial role in the design of transportation and telecommunication networks. In transportation networks, relays are strategic locations where exchange of drivers, trucks or mode of transportation takes place. In green transportation, relays become the refueling/recharging stations that extend the reach of alternative fuel vehicles. In telecommunication networks, they are regenerators extending the reach of optical signals. We first study the network design problem with relays and present a multi-commodity flow formulation and a branch-and-price algorithm to solve it. Motivated by the practical applications, we investigate the special case where each demand has a common designated source. In this special case, we can show that there exists an optimal design that is a tree. Using this fact, we replace the multi-commodity flow formulation with a tree formulation enhanced with Steiner cuts. Employing a branch-and-price-and-cut schema on this formulation, we are able to further extend computational efficiency to solve large problem instances. In a second study, we consider a relay location problem with routing. In particular, we locate refueling stations to maximize the alternative fuel vehicle flow while respecting the range limitations of vehicles and preferences of drivers. We develop a novel model, analyze the polyhedral properties and propose a branch-and-cut algorithm as an exact solution methodology. Extensive computational experiments show that the algorithm significantly improves the solution times compared to previous exact solution methods and extends the sizes of the instances solved to optimality. Finally, we present a robust optimization approach to incorporate traffic demand uncertainty to the relay location problem with routing.